# Expected valued in decision making

Published 16 Feb 2017

#### The expected value according is “the mathematical expected value of a random variable. Equals the sum (or integral) of the values that are possible for it, each multiplied by its probability.” It is also equal to the mean.

Taking an example of a small businessman who wants to place bids for contracts from two subsidiary companies. Placing bids for contracts form two subsidiary disqualifies the businessman form placing bids for contracts in the other subsidiary. Each subsidiary have three contracts with different pay offs to the businessman. Thus the businessman has to make a decision to place bids in which subsidiary. The pay offs from the contract form each subsidiary and the probation of the businessman winning the contract is given US. Subsidiary1 contract A: pay off \$1500 probability 0.5, contract B: \$1000 probability 0.25 contract C \$400 probability 0.25 Subsidiary 2: Contract A payoff \$900 probability 0.25, Contract B; Payoff \$400 and probability 0.25, contract C pay off \$600 probability 0.25. The expected value of the contract will be calculated as : Subsidiary: 1 1500(0.5) + 1000(0.25) + 400(0.25) = \$1100

Subsidiary 2: 900(0.5) + 400(0.25) + 6-00 (0.25) = \$700. The expected value for contracts in subsidiary 1 is greater than expected value of contracts in subsidiary 2. Thus the business will be able to make a decision of which subsidiary to place bids with.

Expected value shows the average outcome of events. It helps a decision maker to know the expected results form the various alternatives that are there. Knowing the expected outcome helps decision maker to make choices between two or several alternatives. In business context the expected value will help a decision maker to make a choice between different investment decisions, contracts to be pursued or to make a choice on different financing options. It can also help the business person make a decision on the divided policy. Expected value analysis can also help an organization to make a decision on projects to pursue.

1. The option from which a decision makes chooses a course of action are called the decision alternatives. Each decision to be made have several alternatives from which the decision maker chooses one depending on the expected value, net, present values, preferences or sensitivity to risks.
2 A pay off is always measured in profit. Pay off represent the benefit the decision makers derives from making a certain decision or from taking a certain option of the available decision alternatives.
3 A decision tree arranges decision alternatives and state of nature in their natural chronological order. As the decision tree arranges events the way they actually take place,. This is important because an event, either a state of nature or a decision is always affected by the events that had happened earlier and it affects the events that happen later. Thus arranging decision alternatives and state of nature in their natural chronological order helps to show the true or actual sequence of events and their interrelationships.
4 Sensitivity analysis considers changes in the available alternatives. Sensitivity analysis is concerned with the analysis of changes in the parameters of an alternative.
5. If p(high) = .3 P(low) = .7, P(favorable high) = .9 and p (unfavorable low) = 6 then p(favorable)= .22

P(high) x p(favorable high)
0.3 x 0.9 = 0.27
= 0.27

6. Lakewood fashion has to decide how many lots of assorted ski wear to order for its three stores. With a payoff table of
Order low medium high
1 lot 12 15 15
2 lots 9 25 35
3 lots 6 35 60

An optimist will advise the Lakewood fashion to make a decision of ordering for three lots. This is because an optimist will have the hope of getting the greatest payoff. 3 lots offer the highest payoff among all the other lots. An optimist always chooses the decision that offers the highest profit.

7. Lakewood fashion has to decide how many lots of assorted ski wear to order for its three stores. With a payoff table of

S1 S2 S3
D1 10 8 6
D2 14 15 2
D3 7 8 9

A conservative will make a decision to choose 1 lot. 1 lot offers the highest profit among the lowest profits offered by the various decisions.

8. Lakewood fashion has to decide how many lots of assorted ski wear to order for its three stores. With a payoff table of

S1 S2 S3
D1 10 8 6
D2 14 15 2
D3 7 8 9

A minmax will make a decision to choose 1 lot. 1 lot offers the highest profit and has the highest regret offered by the various decisions.

A pay off table given an
S1 S2 S3
D1 10 8 6
D2 14 15 2
D3 7 8 9
An optimist decision maker will choose decision D2
S1 S2 S3 Highest
D1 10 8 6 10
D2 14 15 2 15
D3 7 8 9 9

This is because decision D2 has the highest pay off among all the other decisions.

A pay off table given as

S1 S2 S3 Lowest payoffs
D1 10 8 6 6
D2 14 15 2 2
D3 7 8 9 7

A conservative decision maker will choose decision d3. This is because it is the decision with the best pay off among the worst payoffs of all the decisions.

### Reference:

Glossary: Equivalent value. Retrieved on January 23, 2008